| A 2-D, two- and three-layer stratified airflow over a
mountain of arbitrary shape is considered on the assumptions that
upstream wind velocity and static stability within each layer are
constant (Long's model). The stratosphere is simulated by
an infinitely deep upper layer with enhanced static stability.
The analytical solution for the stream function, as well as first
(linear) and second order approximations to the wave drag, are
obtained in hydrostatic limit N1L/U0→∞, where N1
is the Brunt-Väsälä frequency in the troposphere, L is a
characteristic length of the obstacle, and U0 is upstream
velocity. The results of numerical computations show the principal
role of long waves in the process of interaction between the model
layers for a typical mesoscale mountains for which the hydrostatic
approximation proves valid in a wide range of flow parameters, in
accordance with the earlier conclusions of Klemp and Lilly (1975). Partial reflection of wave energy from the tropopause produces strong
influence on the value of wave drag for typical middle and upper
tropospheric lapse rates, leading to a quasi-periodic dependance of
wave drag on a reduced frequency
( is tropopause height) in the troposphere. The flow
seems to be statically unstable for k≥2 for sufficiently
large obstacles (whose height exceeds 1 km). In this case,
vast regions of rotor motions and strong turbulence are predicted
from model calculations in the middle troposphere and the lower
stratosphere. The model calculations also point to a testify for possible
important role of nonlinear effects associated with finite height
of the mountain on the conditions of wave drag amplification in
the process of overflow of real mountains. |